{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression (Basic - ANG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam1</th>\n",
       "      <th>Exam2</th>\n",
       "      <th>Admitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Exam1      Exam2  Admitted\n",
       "0  34.623660  78.024693         0\n",
       "1  30.286711  43.894998         0\n",
       "2  35.847409  72.902198         0\n",
       "3  60.182599  86.308552         1\n",
       "4  79.032736  75.344376         1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('logreg1',names=['Exam1','Exam2','Admitted'])\n",
    "\n",
    "df.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam1</th>\n",
       "      <th>Exam2</th>\n",
       "      <th>Admitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>65.644274</td>\n",
       "      <td>66.221998</td>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>19.458222</td>\n",
       "      <td>18.582783</td>\n",
       "      <td>0.492366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>30.058822</td>\n",
       "      <td>30.603263</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>50.919511</td>\n",
       "      <td>48.179205</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>67.032988</td>\n",
       "      <td>67.682381</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>80.212529</td>\n",
       "      <td>79.360605</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>99.827858</td>\n",
       "      <td>98.869436</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Exam1       Exam2    Admitted\n",
       "count  100.000000  100.000000  100.000000\n",
       "mean    65.644274   66.221998    0.600000\n",
       "std     19.458222   18.582783    0.492366\n",
       "min     30.058822   30.603263    0.000000\n",
       "25%     50.919511   48.179205    0.000000\n",
       "50%     67.032988   67.682381    1.000000\n",
       "75%     80.212529   79.360605    1.000000\n",
       "max     99.827858   98.869436    1.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# EDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(df['Exam1'],label='Ex1')\n",
    "sns.distplot(df['Exam2'],label='Ex2')\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1850fa7efd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df['Exam1'],df['Exam2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1850fb364f0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.countplot(df['Admitted'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Let's observe the score pattern of who's admitted and who's not.\n",
    "d_0 = df[df['Admitted'] == 0]\n",
    "\n",
    "d_1 = df[df['Admitted'] == 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "106.65269319478824"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_0['Exam1'].mean() + d_0['Exam2'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "148.67532477920798"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_1['Exam1'].mean() + d_1['Exam2'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#So, clearly, the selected candidates beat the non selected ones pn score by a huge margin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'The Sigmoid Function')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10,10,100)\n",
    "\n",
    "y = 1/(1 + np.exp(-x))\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.grid()\n",
    "plt.title('The Sigmoid Function')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18510cefaf0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "sns.scatterplot(df['Exam1'], df['Exam2'], hue=df['Admitted'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#So basically we have to find the decision boundary in this case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Let's create a function for sigmoid\n",
    "\n",
    "def sigmoid(x):\n",
    "    \n",
    "    s = 1 / (1 + np.exp(-x))\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10,10)\n",
    "\n",
    "y = sigmoid(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sigmoid(0) should exactly give you 0.5. Let's test that out. \n",
    "sigmoid(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cost Function and Gradient.\n",
    "\n",
    "### $ Z = \\theta^{T} X $\n",
    "\n",
    "### $ h_{\\theta}(X) = \\sigma(Z) $\n",
    "\n",
    "### $ J(\\theta) = \\frac{1}{m} \\sum [-y log(h_{\\theta}(x)) -(1-y)log(1 - h_{\\theta}(x) ] $\n",
    "\n",
    "### $ \\frac {\\partial J(\\theta)}{\\partial \\theta} = \\frac{1}{m} \\sum [(h_{\\theta}(x) -y) * x ] $\n",
    "\n",
    "Note that the Gradient Formula is very similar to the Linear Regression Problem. \n",
    "Just that the Definition of h(x) is different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Our z looks Like this - Z = a + bx1 + cx2\n",
    "x0 = np.ones(len(df))\n",
    "x1 = np.array(df['Exam1'])\n",
    "x2 = np.array(df['Exam2'])\n",
    "\n",
    "X = np.zeros((100,3))\n",
    "\n",
    "X[:,0] = x0\n",
    "X[:,1] = x1\n",
    "X[:,2] = x2\n",
    "\n",
    "# X.shape -- 100x3\n",
    "\n",
    "y = np.array(df['Admitted']).reshape(100,1)\n",
    "\n",
    "# y.shape\n",
    "\n",
    "# X.shape\n",
    "\n",
    "# theta = np.zeros((3,1))\n",
    "\n",
    "# Z = np.dot(X,theta)\n",
    "\n",
    "# Z.shape -- 100x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(theta,X,y):\n",
    "    \n",
    "    #let's say theta is 3x1\n",
    "    #X is 100x3\n",
    "    #therefore z is (100x3)*(3x1) = 100x1\n",
    "    \n",
    "    Z = np.dot(X,theta)\n",
    "    \n",
    "    h = sigmoid(Z)\n",
    "    \n",
    "    m = 100\n",
    "    \n",
    "    L = y*np.log(h) + (1-y)*np.log(1 - h)\n",
    "    \n",
    "    J = -1*(1/m)*np.sum(L)\n",
    "    \n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's see how far off reality we are with an initial guess of parameters.\n",
    "theta = np.zeros((3,1))\n",
    "\n",
    "cost(theta,X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### $ \\frac {\\partial J(\\theta)}{\\partial \\theta} = \\frac{1}{m} \\sum [(h_{\\theta}(x) -y) * x ] $\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Gradient\n",
    "\n",
    "def gradient(theta , X, y):\n",
    "    \n",
    "    #Note-\n",
    "    #1. theta - 3x1\n",
    "    #2. X - 100x3\n",
    "    #3. y = 100x1\n",
    "    #4. h = 100x1\n",
    "    # (h - y) - 100x1 - T - 1x100 dot 100x3 -- 1x3\n",
    "    g = np.zeros(theta.shape)\n",
    "    \n",
    "    Z = np.dot(X,theta)\n",
    "    \n",
    "    h = sigmoid(Z)\n",
    "    \n",
    "    m = len(X)\n",
    "    \n",
    "    \n",
    "    dg0 = (1/m)*np.sum((h-y)*(X[:,0].reshape(100,1)))\n",
    "    dg1 = (1/m)*np.sum((h-y)*(X[:,1].reshape(100,1)))\n",
    "    dg2 = (1/m)*np.sum((h-y)* (X[:,2].reshape(100,1)))\n",
    "    \n",
    "    g[0] = dg0\n",
    "    g[1] = dg1\n",
    "    g[2] = dg2\n",
    "\n",
    "                         \n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gradient(theta,X,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # import scipy.optimize as opt\n",
    "# theta = np.zeros((3,1))\n",
    "# l = []\n",
    "# for e in range(100000):\n",
    "\n",
    "#     c = cost(theta,X,y)\n",
    "    \n",
    "#     theta = theta - 0.01*gradient(theta,X,y)\n",
    "    \n",
    "#     l.append(c)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt\n",
    "# theta= np.zeros((3,1))\n",
    "res = opt.minimize(fun=cost, x0=theta, args=(X, y), method='Newton-CG', jac=gradient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 68.58826104524884\n",
       "     jac: array([  6.8928685 , -92.00156937,  -7.60471491])\n",
       " message: 'Warning: Desired error not necessarily achieved due to precision loss.'\n",
       "    nfev: 20\n",
       "    nhev: 0\n",
       "     nit: 1\n",
       "    njev: 12\n",
       "  status: 2\n",
       " success: False\n",
       "       x: array([4.60628373e-05, 5.53178590e-03, 5.18798469e-03])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.0016695],\n",
       "       [ 0.009763 ],\n",
       "       [ 0.0011226]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "yp = np.dot(X,theta)\n",
    "\n",
    "df['Pred. Probs'] = yp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam1</th>\n",
       "      <th>Exam2</th>\n",
       "      <th>Admitted</th>\n",
       "      <th>Pred. Probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "      <td>0.423952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "      <td>0.343296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "      <td>0.430149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "      <td>0.682783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "      <td>0.854509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>83.489163</td>\n",
       "      <td>48.380286</td>\n",
       "      <td>1</td>\n",
       "      <td>0.867747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>42.261701</td>\n",
       "      <td>87.103851</td>\n",
       "      <td>1</td>\n",
       "      <td>0.508714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>99.315009</td>\n",
       "      <td>68.775409</td>\n",
       "      <td>1</td>\n",
       "      <td>1.045150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>55.340018</td>\n",
       "      <td>64.931938</td>\n",
       "      <td>1</td>\n",
       "      <td>0.611508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>74.775893</td>\n",
       "      <td>89.529813</td>\n",
       "      <td>1</td>\n",
       "      <td>0.828874</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Exam1      Exam2  Admitted  Pred. Probs\n",
       "0   34.623660  78.024693         0     0.423952\n",
       "1   30.286711  43.894998         0     0.343296\n",
       "2   35.847409  72.902198         0     0.430149\n",
       "3   60.182599  86.308552         1     0.682783\n",
       "4   79.032736  75.344376         1     0.854509\n",
       "..        ...        ...       ...          ...\n",
       "95  83.489163  48.380286         1     0.867747\n",
       "96  42.261701  87.103851         1     0.508714\n",
       "97  99.315009  68.775409         1     1.045150\n",
       "98  55.340018  64.931938         1     0.611508\n",
       "99  74.775893  89.529813         1     0.828874\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.linspace(0.40,0.80,100)\n",
    "a = []\n",
    "for b in v:\n",
    "    #\n",
    "    label = lambda t : 1 if t>b else 0\n",
    "    df['yp'] = df['Pred. Probs'].apply(label)\n",
    "    a.append(len(df[df['yp'] == df['Admitted']]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x223a8087f10>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# df['yp'] = df['Pred. Probs'].apply(label)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(v,a,lw = 3)\n",
    "plt.grid()\n",
    "plt.axhline(y = max(a),color='r',lw = 5,label='Max Accuracy = 83%')\n",
    "plt.axvline(x=0.60 , color='g',lw=3)\n",
    "\n",
    "plt.title('Hyper-Parameter tuning to Optimize Decision Boundary')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# len(df[df['yp'] == df['Admitted']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "z = np.linspace(-10,10)\n",
    "s = 1/(1 + np.exp(-z))\n",
    "\n",
    "plt.plot(z,s)\n",
    "plt.axhline(y = 0.60,color='red',lw=5)\n",
    "\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.0016695],\n",
       "       [ 0.009763 ],\n",
       "       [ 0.0011226]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sns.scatterplot(df['Exam1'] , df['Exam2'],hue=df['Admitted'])\n",
    "# plt.plot(df['Exam1'] , boundary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1., 1.],\n",
       "        [1., 1.],\n",
       "        [1., 1.]],\n",
       "\n",
       "       [[1., 1.],\n",
       "        [1., 1.],\n",
       "        [1., 1.]],\n",
       "\n",
       "       [[1., 1.],\n",
       "        [1., 1.],\n",
       "        [1., 1.]],\n",
       "\n",
       "       [[1., 1.],\n",
       "        [1., 1.],\n",
       "        [1., 1.]]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w1 = np.ones((4,3))\n",
    "\n",
    "w2 = np.ones((4,3))\n",
    "\n",
    "W = np.array([w1 , w2]).reshape(4,3,2)\n",
    "\n",
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.ones((3,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]]\n"
     ]
    }
   ],
   "source": [
    "print(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
